Preheat oven to 400 degrees F and grease muffin tins with butter.
In a large bowl, sift together flour, baking power, baking soda, sugar, and salt.
In a medium sized pan over medium heat, melt the butter. Swirl occasionally to ensure butter is cooking evenly. As the butter melts, it will begin to foam and the color will get darker. Scrape bottom to release any browned specs. Once you start smelling the nutty aroma, remove browned butter from heat and allow to cool.
In a separate bowl, whisk eggs, buttermilk, vanilla, and mostly cooled browned butter together. Make a well in the dry ingredients and pour in the liquid ingredients. Fold together and do not over mix. Fold in the blueberries.
Spoon batter into greased muffin tins and bake in preheated oven until golden brown, about 20-30 minutes (mine took longer because I used a stone muffin pan). When done cooking, immediately remove from muffin tins and allow to cool on cooling rack.